Write a slope intercept equation for the line with the slope-1/4 and y-intercept (0,-2)and graph the line.Please show work.
To find the slope-intercept equation of a line, you need to use the formula:
y = mx + b,
where m represents the slope of the line, and b represents the y-intercept. Now, let's solve step-by-step:
Step 1: Plug in the given values
m = -1/4 (slope)
b = -2 (y-intercept)
Step 2: Substitute the values into the formula:
y = (-1/4)x - 2
Thus, the slope-intercept equation for the given line is y = (-1/4)x - 2.
To graph the line, you can start by plotting the y-intercept, which is a point on the line when x = 0. In this case, the y-intercept is (0, -2).
Next, use the slope to determine additional points on the line. The slope -1/4 means for every increase of 1 in the x-coordinate, the y-coordinate decreases by 1/4.
Using this information, you can select any additional x-value and calculate its corresponding y-value. For example, if we let x = 4:
y = (-1/4)(4) - 2
y = -1 - 2
y = -3
So another point on the line is (4, -3).
You can continue this process to find more points or simply connect the initial point (0,-2) and (4,-3) with a straight line.
Once you have plotted two or more points, connect them to form a straight line. The graph of the line with the given slope-intercept equation y = (-1/4)x - 2 will look like this:
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